Question

initial knowledge check
question 14
fill in the ( p(x = x) ) values to give a legitimate probability distribution for the discrete random variable ( x ), whose possible values are 2, 3, 4, 5, and 6.

value ( x ) of ( x )	( p(x = x) )
3	0.25
4	0.23
5
6

Explanation:

Step1: Sum known probabilities

$0.27 + 0.25 + 0.23 = 0.75$

Step2: Calculate remaining total probability

$1 - 0.75 = 0.25$

Step3: Assign equal values (valid split)

For a legitimate distribution, we can split the remaining probability equally between $x=5$ and $x=6$ (any non-negative values summing to 0.25 are valid; equal split is standard here):
$P(X=5) = \frac{0.25}{2} = 0.125$
$P(X=6) = \frac{0.25}{2} = 0.125$

Answer:

For $x=5$, $P(X=x)=0.125$; for $x=6$, $P(X=x)=0.125$
(Note: Any pair of non-negative numbers that add to 0.25 is also a valid solution, but equal division is a standard legitimate choice.)